ABC News said a private memorial service limited to family and close friends would take place on Thursday.

Reynolds's son Todd Fisher told ABC's "20/20" on Friday he was planning a joint service at Forest Lawn Memorial Park in the Hollywood Hills with the help of Billie Lourd, his niece and Carrie Fisher's daughter.

The Hollywood Reporter quoted a family source as confirming there would also be an event at the Beverly Hills compound where Reynolds and Fisher were neighbors.

"I'm not sure what they're calling it -- a funeral or a wake -- but it will be Thursday at the house," the source said.

"It will be exactly what they both wanted, to be together."

The family is understood to be discussing a public memorial, although no plans have been announced.

Silent film star Buster Keaton, Oscar-winning Rod Steiger and David Carrandine, the star of "Kung Fu" and Quentin Tarantino's "Kill Bill" films, are also buried there.

Reynolds, who tap-danced her way into American hearts as a star of "Singin' in the Rain," died on Wednesday last week, a day after daughter Carrie Fisher's death.

The 84-year-old suffered a stroke at the Beverly Hills compound as she was making funeral arrangements for Fisher, who had suffered a heart attack.

"She didn't die of a broken heart. She just left to be with Carrie," Todd Fisher told "20/20."

Fisher, who catapulted to worldwide stardom as rebel warrior Princess Leia in the original "Star Wars" trilogy, died in Los Angeles four days after suffering a heart attack on a transatlantic flight. She was 60.

Lourd opened up on Monday about losing her mother and grandmother just a day apart, telling her Instagram followers their prayers and kind words had given her strength "during a time I thought strength could not exist."

"There are no words to express how much I will miss my Abadaba and my one and only Momby. Your love and support means the world to me," the 24-year-old wrote.

"Bright Lights: Starring Carrie Fisher and Debbie Reynolds," a documentary about Reynolds's at-times rocky relationship with her daughter, premiered at this year's Cannes Film Festival and is due to air on HBO on Saturday.